CIELAB Color Space by Esteban Jacobo

Gernot Hoffmann CIELab Color Space

Contents 1. Introduction

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Formulas Primaries and Matrices Gamut Restrictions and Tests Inverse Gamma Correction CIE L*=50 NTSC L*=50 sRGB L*=1/10/.../90/99 AdobeRGB L*=10/.../90 ProPhotoRGB L*=10/.../90 3D Views Linear and Standard Nonlinear CIELab Human Gamut in CIELab Low Chromaticity sRGB L*= 50 with RGB Numbers PostScript Kernels Mapping CIELab to xyY Number of Different Colors HLS-Hue for sRGB in CIELab References

2 4 10 11 12 13 14 15 26 35 44 47 48 49 50 51 56 59 60 62

1.1 Introduction CIE XYZ is an absolute color space (not device dependent). Each visible color has non-negative coordinates X,Y,Z. CIE xyY, the horseshoe diagram as shown below, is a perspective projection of XYZ coordinates onto a plane xy. The luminance is missing. CIELab is a nonlinear transformation of XYZ into coordinates L*, a*,b*. The gamut for any RGB color system is a triangle in the CIE xyY chroma足足ticity diagram, here shown for the CIE primaries, the NTSC primaries, the Rec.709 primaries (which are also valid for sRGB and therefore for many PC monitors) and the non-physical working space ProPhotoRGB. The white points are individually defined for the color spaces. The CIELab color space was intended for equal perceptual differences for equal changes in the coordinates L*, a* and b*. Color differences deltaE are defined as Euclidian distances in CIELab. This document shows color charts in CIELab for several RGB color spaces. .0 y

sRGB uses ITU-R BT.709 primaries Red Green Blue White x 0.64 0.30 0.15 0.3127 y 0.33 0.60 0.06 0.3290 AdobeRGB uses Red and Blue like sRGB and Green like NTSC CIE-RGB are the primaries for color matching tests: 700 /546.1/435.8nm

0.9 ProPhoto 520 525 5 5 530

0.8

535 540

5 0

545

0.7

550 555

505

560

0.6

565 570

500

0.5 0.4 0.3 0.2

NTSC CIE

575

sRGB

580 585 590 595 600 605 6 0 620 635 700

495

490

Wavelengths in nm

485

Purple line

480

0. 0.0 0.0

475 470 460 380

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 x .0

1.2 Introduction CIELab uses new coordinates L*,a* and b* by functions as described in the next chapter. The true shape of the human gamut in CIELab is shown in chapter 13. This results in huge areas for higher luminance. Just to show the orientation together with the gamut triangle for the primaries we proceed as follows: Convert the contour points x,y for Y=1 into RGB. Divide R,G,B by the maximum of R,G,B. Convert R,G,B to L*,a*,b*. The gamut triangle in x yY has to be replaced by a representation of a color cube with corners R,G,B and Y(yellow),C,M. The gray axis is at a*= b*= 0. Therefore the area is confined by a distorted hexagon. A similar diagram can be found in [1]. Later it will be shown that the actual gamut, which depends on the luminance, is a smaller area inside the hexagon.

-250 -225 -200 - 75 - 50 - 25 - 00 -75 -50 -25 0

25 50 75 00 25 50 75 200 225 250

250

225

200

Green

Red 75

-25

-50

-75

- 00 - 25

Gamut

- 00

CIE primaries WP Eq.Energy

- 25

- 50 - 75 -200 -225

- 50

Blue

- 75

Contour for R-Y-G-C-B-M-R hexagon Outer blue area human gamut

-200 -225

-250

-250 -250 -225 -200 - 75 - 50 - 25 - 00 -75 -50 -25 0

25 50 75 00 25 50 75 200 225

2.1 Formulas / From RGB’ to CIELab R´G´B´ are nonlinearly distorted values for each channel in physical tristimulus systems like CIE, NTSC or working spaces like sRGB or AdobeRGB(98). RGB are undistorted values which are linearly related to CIEXYZ. Each RGB system has a white point(w). The transformation to CIELab requires a reference white point (n) which is either (w) or D50. Issues of adaptation are taken into account by the linearized Bradford transform. The Bradford matrix maps the XYZ-values for a color in e.g. D65 to another set in D50. The colors should look alike under D65 for the first set and under D50 for the second. C

C'G

sRGB gamma correction, C =R,G,B Generic gamma correction, G = 2.2, C =R,G,B i f C ' ≤ 0.03928   C '/ 2.92 C =   2.4 ((0.055 + C ') / .055) else   RGB to XYZ ( same white point D65 ) X = C xr R RGB to XYZ ( new white point D50, Bradford correction ) X = B C xr R XYZ to L*a*b* ( reference white X n ) X X = Xn Y Y = Yn Z Z = Zn  X 3 i f X > 0.008856  X =   else 7.787 X + 6 6   Y 3 i f Y > 0.008856  Y =   else 7.787 Y + 6 6   Z 3 i f Z > 0.008856  Z =   else 7.787 Z + 6 6  L* = a* = b* =

6 Y − 6 500 ( X − Y ) 200 ( Y − Z )

2.2 Formulas / From CIELab to RGB’ Please refer to explanations on the previous page. A value RGB is out of gamut if any of the numbers is less than 0 or greater than 1 (normalized values). L*a*b* to XYZ Y = (L* + 6) / 6 X =

a* / 500 + Y

Z = − b* / 200 + Y

 X 3 if X > 0.206893    (X − 6 6) / 7.787 else   Y 3 if Y > 0.206893    (Y − 6 6) / 7.787 else   Z 3 if Z > 0.206893    (Z − 6 6) / 7.787 else  X n X

Yn Y

Z n Z

X = Y = Z =

XYZ to RGB ( same white point D50) R

− Crx X = C xr X

XYZ to RGB (new white point D65, Bradford correction) R

( BC xr ) − X = Crx B − X

Generic gamma correction, G = 2.2, C = R,G,B C' =

C / G

sRGB gamma correction, C= R,G,B C' =

 2.92C if C ≤ 0.00304    2.4 − 0.055 else   .055 C

2.3 Formulas / From xyY to XYZ The CIE chromaticity diagram is called xyY. The threedimensional space is called XYZ. xyY to XYZ z X Z

= = =

− x − y Yx/y Yz/y

XYZ to xyY D x y z

= = = =

X+Y+Z X/D Y/D Z /D

Some important numbers 3

0.008856 = 0.2068930

6 / 6

= 0. 3793

6 ⋅ 0.008856 3

− 6 = 903.3 ⋅ 0 .008856 = 8.0

2.4 Formulas / Structure of the Conversion The conversion from XYZ to L*a*b* consists essentially of four steps: 1. White point correction 2. Nonlinear distortion of the variables X,Y, Z by a cubic root 3. Linear transformation into a new vector basis c, a, b 4. Scaling With some obvious simplifications the linear part can be written by matrices: X   0  L  Y  =  0 0  A   Z   0 −  B  X       0  Y  = L   + A  0  + B  0  = L c + A a + B b  Z    0  −  L   0 0  X A  =  − 0   Y  B   0 −   Z 

c Y

X,a b Base vector a points into X-direction, b into negative Z-direction and c is along the diagonal in XYZ. L, A and B are normalized substitutes for L*, a* and b*.

2.5 Formulas / Matrix Calculation Matrices for Primaries and White Point [3]

X  Y  = C x r  Z 

R   G  B 

R  X   G = C r x  Y   B   Z  D U V

= (x r − x b )(y g − y b ) − (y r − y b )(x g − x b ) = (x w − x b )(y g − y b ) − (yw − y b )(x g − x b ) = (x r − x b )(yw − y b ) − (y r − y b )(x w − x b )

u v w

= U/D = V/D = − u − v

Cxr

u x r / yw = u y r / yw  u z r / yw

v x g / yw v y g / yw v z g / yw

w x b / yw w y b / yw w z b / yw

   

Cr x = C −x r In the next formulas use c xr ik for c ik D = c (c 22 c 33 − c 23 c 32 ) − c 2 (c 2 c 33 − c 23 c 3 ) + c 3 (c 2 c 32 − c 22 c 3 ) c rx = ( c 22 c 33 − c 23 c 32 ) / D c rx 2 = ( c 2 c 33 − c 3 c 32 ) / D c rx 3 = ( c 2 c 23 − c 3 c 22 ) / D c rx 2 = ( c 2 c 33 − c 23 c 3 ) / D c rx 22 = ( c c 33 − c 3 c 3 ) / D c rx 23 = ( c c 23 − c 3 c 2 ) / D c rx 3 = ( c 2 c 32 − c 22 c 3 ) / D c rx 32 = ( c c 32 − c 2 c 3 ) / D c rx 33 = ( c c 22 − c 2 c 2 ) / D

2.6 Formulas / Bradford Matrix Calculation Bradford matrix calculation, based on [8] zn Yn Xn Zn

= = = =

− xn − yn Yn x n / y n Yn z n / y n

zw Yw Xw Zw

= = = =

− xw − yw Yw x w / y w Yw z w / y w

Cone response  +0.895 +0.2664 −0. 6 4  Mcx =  −0.7502 + .7 35 +0.0367   +0.0389 −0.0685 + .0296  Cn Cw

ρ n  =  γ n  = Mcx X n βn  ρ w  =  γ w  = Mcx X w β w  ρ n / ρ w =  0  0

0 γn / γ w 0

0  0  βn / β w 

Bradford matrix − = Mcx D Mcx

The matrices↔ CxrD50 and w on the next page contain the XYZ coordinates of the RGB primaries. E.g. for n ↔ D65 The X first = column B X delivers the base vector R in XYZ, the second G and the third B. D50

D65

For ICC profiles the matrices are multiplied by the Bradford matrix B. Then the base vectors mean ’adapted primaries’. The original primaries under D65 (sRGB, AdobeRGB(98)) should look alike the adapted primaries under D50. This can easily lead to confusions. We use strictly ’not-adapted’ primaries and consider the Bradford transformation as an additional feature which can be applied. This should not change physical primaries or working space primaries.

3. Primaries and Matrices For sRGB (709 primaries) the exponent gamma is 2.4, but because of a linear slope the effective gamma is 2.2 . The white point for NTSC is Illuminant C, 6774K. CIE RGB R G B W N

x 0.7347 0.2738 0. 666 0.3333 0.3457

WP=Eq.Energy y 0.2653 0.7 74 0.0089 0.3333 0.3585

R G B W N

Z 0.0000 0.0 00 0.9903 .0003 0.825

Matrix Crx 2.3650 -0.8967 -0.468 -0.5 5 .4264 0.0887 0.0052 -0.0 44 .0089

Matrix Cxr 0.4899 0.3 00 0. 769 0.8 24 0.0000 0.0 00

0.200 0.0 06 0.9903

Matrix Crx .3458 -0.2556 -0.05 -0.5446 .5083 0.0205 0.0000 0.0000 .2 20

Matrix B 0.9979 -0.004 -0.0295 -0.0097 .0 83 -0.0086 -0.0074 0.0 35 0.8 88

Matrix B-inv .0024 0.0036 0.0096 0.9820 0.0089 -0.0 6

0.036 0.0 06 .22 4

Matrix B .0000 -0.0000 0.0000 0.0000 .0000 -0.0000 -0.0000 0.0000 .0000

x 0.6700 0.2 00 0. 400 0.3 00 0.3457

WP=NTSC y z 0.3300 -0.0000 0.7 00 0.0800 0.0800 0.7800 0.3 60 0.3740 0.3585 0.2958

y 0.2653 0.8404 0.000 0.3585 0.3585

WideGamut RGB

G=2.2 X 0.6070 0. 734 0.2006 0.98 0 0.9643

x 0.7347 0. 596 0.0366 0.3457 0.3457

Y Z 0.2990 -0.0000 0.5864 0.066 0. 46 . 75 .0000 . 835 .0000 0.825

R G B W N

x 0.7347 0. 52 0. 566 0.3457 0.3457

y 0.2653 0.8264 0.0 77 0.3585 0.3585

z 0.0000 0.0000 0.9633 0.2958 0.2958

z 0.0000 0.0584 0.8257 0.2958 0.2958

0.2006 0. 46 . 75

Matrix Crx .4622 -0. 845 -0.2734 -0.5228 .4479 0.0682 0.0346 -0.0958 .2877

Matrix B .0377 0.0 54 -0.0584 0.0 70 .0057 -0.0 89 -0.0 20 0.0205 0.6898

Matrix B-inv 0.9648 -0.0 64 -0.0 60 0.994 0.0 73 -0.0298

0.08 2 0.0259 .4503

Matrix B .0000 -0.0000 0.0000 0.0000 .0000 -0.0000 -0.0000 0.0000 .0000

x 0.6400 0.3000 0. 500 0.3 27 0.3457

y 0.3300 0.6000 0.0600 0.3290 0.3585

WP=D65

Y 0.2 26 0.7 52 0.0722 .0000 .0000

Z 0.0 93 0. 92 0.9505 .089 0.825

Matrix Crx 3.24 0 - .5374 -0.4986 -0.9692 .8760 0.04 6 0.0556 -0.2040 .0570

Matrix Cxr 0.4 24 0.3576 0.2 26 0.7 52 0.0 93 0. 92

0. 805 0.0722 0.9505

Matrix B .0479 0.0229 -0.0502 0.0296 0.9904 -0.0 7 -0.0092 0.0 5 0.75 9

Matrix B-inv 0.9555 -0.023 -0.0284 .0 00 0.0 23 -0.0205

0.0633 0.02 0 .3304

x 0.6400 0.2 00 0. 500 0.3 27 0.3457

y 0.3300 0.7 00 0.0600 0.3290 0.3585

z 0.0300 0. 000 0.7900 0.3583 0.2958

OptiRGB

G=2.4 X 0.4 24 0.3576 0. 805 0.9505 0.9643

WP=D65 z 0.0300 0.0800 0.7900 0.3583 0.2958

R G B W N

G=2.2 X 0.5767 0. 856 0. 882 0.9505 0.9643

Y 0.2973 0.6274 0.0753 .0000 .0000

Z 0.0270 0.0707 0.99 3 .089 0.825

Matrix Crx 2.04 6 -0.5650 -0.3447 -0.9692 .8760 0.04 6 0.0 34 -0. 84 .0 52

Matrix Cxr 0.5767 0. 856 0.2973 0.6274 0.0270 0.0707

0. 882 0.0753 0.99 3

Matrix B .0479 0.0229 -0.0502 0.0296 0.9904 -0.0 7 -0.0092 0.0 5 0.75 9

Matrix B-inv 0.9555 -0.023 -0.0284 .0 00 0.0 23 -0.0205

0.0633 0.02 0 .3304

x 0.6658 0. 929 0. 355 0.3 27 0.3457

G= .8 X 0.7978 0. 352 0.03 3 0.9643 0.9643

Y 0.288 0.7 8 0.000 .0000 .0000

Z 0.0000 0.0000 0.825 0.825 0.825

Matrix Cxr 0.7978 0. 352 0.288 0.7 8 0.0000 0.0000

0.03 3 0.000 0.825

Matrix B-inv .0000 0.0000 -0.0000 -0.0000 .0000 0.0000 0.0000 0.0000 .0000

WP=D50

Matrix Cxr 0.6070 0. 734 0.2990 0.5864 -0.0000 0.066

AdobeRGB(98) R G B W N

R G B W N

Matrix Crx .9097 -0.5324 -0.2882 -0.9850 .9998 -0.0283 0.0582 -0. 82 0.8966

sRGB 709 primaries R G B W N

X 0.4899 0.3 00 0.200 .0000 0.9643

WP=D50

Y 0. 769 0.8 24 0.0 06 .0000 .0000

NTSC RGB

z 0.0000 0.0088 0.8246 0.3334 0.2958

ProPhoto RGB

G=2.2

G=2.2 X 0.7 65 0. 0 0 0. 468 0.9643 0.9643

Y 0.2587 0.7247 0.0 65 .0000 .0000

Z 0.0000 0.05 2 0.7739 0.825 0.825

Matrix Cxr 0.7 65 0. 0 0 0.2587 0.7247 0.0000 0.05 2

0. 468 0.0 65 0.7739

Matrix B-inv .0000 0.0000 -0.0000 -0.0000 .0000 0.0000 0.0000 0.0000 .0000

WP=D65 y 0.3340 0.78 6 0.0399 0.3290 0.3585

z 0.0002 0.0255 0.8246 0.3583 0.2958

G=2.2 X 0.6 73 0. 576 0. 755 0.9505 0.9643

Y 0.3097 0.6386 0.05 7 .0000 .0000

Z 0.0002 0.0208 .0680 .089 0.825

Matrix Crx .8436 -0.4458 -0.28 4 -0.8954 .7848 0.0608 0.0 7 -0.0347 0.9352

Matrix Cxr 0.6 73 0. 576 0.3097 0.6386 0.0002 0.0208

0. 755 0.05 7 .0680

Matrix B .0479 0.0229 -0.0502 0.0296 0.9904 -0.0 7 -0.0092 0.0 5 0.75 9

Matrix B-inv 0.9555 -0.023 -0.0284 .0 00 0.0 23 -0.0205

0.0633 0.02 0 .3304

4. Gamut Restrictions and Tests Mostly it is assumed that all colors inside the gamut triangle can be shown by the respective device. Actually the gamut in CIELab is not the triangle R-G-B but the hexagon R-Y-G-C-B-M-R. We have to choose an interpolation path which shows also fully saturated yellow, cyan and magenta. In the next diagrams we can see color patches which are out of gamut though they are inside the hexagon. The gamut in the chromaticity diagram is the projection of all available colors in XYZ onto xyY, ignoring the spatial distribution in XYZ. The available gamut depends strongly on the luminance Y. A color is considered as out of gamut if at least one value of R,G,B is larger than one or smaller than zero. The values are clipped for these limits then. Such a color is usually shown by the device reasonably, though slightly wrong. The color charts were tested by Photoshop 7. E.g. the chart sRGB-050 for L*=50. Select sRGB as working space and Rendering Intent Relative Colorimetric. Open document in RGB mode. Place page of PDF. Indicate CIELab values by info palette. Photoshop Relative Colorimetric means ICC Media-Relative Colorimetric.

5. Inverse Gamma Correction RGB values are transformed into nonlinear values R´G´B´ by C´=C1/2.2 for CIE and NTSC primaries. This is a compensation for calibrated monitors. sRGB differs slightly from Gamma =2.2 because the transfer function is composed of a linear part and a Gamma =2.4 part. C´ = 1.055 C 1/2.4 - 0.055 if C > 0.00304 C´ = 12.92 C else The maximal difference is less than 1% full scale. The diagram shows the Gamma corrections instead of the inverse corrections.

Black

C=C´ 2.2

Red

sRGB

Green Ten times the difference

According to profile informations, NTSC, CIE-RGB and AdobeRGB(98) use the simple Gamma correction (no linear part) with G=2.2. ProPhoto uses G=1.8. Gamma encoded values C’, here for gray R’=G’=B’ are nearly a linear function of L*. 255

2.0 .8 Dens .6

RGB’

.4 .2 .0

Black

Linear

Green G=2.5 / uncalibrated monitor

0.8 0.6 0.4

Blue

G=2.2 / calibrated monitor

Red

G=2.4+slope / sRGB

Gray

Density

0.2 0

0 L* 00

6. CIE L*=50 The illustrations were made by PostScript EPS programs as vector graphics Converted to PDF by Acrobat Distiller they are still vector graphics Eventually the appearance can be improved by Smooth Line Art = Off

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 50

-40

CIE primaries White Eq.Energy Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

7. NTSC L*= 50

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 50

-40

NTSC primaries White NTSC Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.1 sRGB L*=1

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* =

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.2 sRGB L*=10

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 0

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.3 sRGB L*=20

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 20

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.4 sRGB L*=30

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 30

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.5 sRGB L*=40

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 40

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.6 sRGB L*=50

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 50

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.7 sRGB L*=60

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 60

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.8 sRGB L*=70

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 70

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.9 sRGB L*=80

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 80

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.10 sRGB L*=90

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 90

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

8.11 sRGB L*=99

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 99

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.1 AdobeRGB L*=10 This chapter contains additionally to the RGB values for AdobeRGB (1998 is omitted here) the CIELab values for the offset printing process ISOcoated_v2_eci.icc [13]. The graphic shows available Lab values as defined by the profile LUT AtoB1. These discrete values are shown as circles either black on light background or white on dark background. The profile has unity input and output curves and an identity matrix. The printable values for L = L*-1 to L* are shown as stroked round dots, those for L=L* to L*+1 are shown as filled round dots. It is obviously not a trivial task to define gamut boundaries formalistically by dominating convex shapes with locally weak concave appearance [12]. Continued next page.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 0

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.2 AdobeRGB L*=20 The CIELab values in the profile LUT AtoB1 are normalized for white at L*=100, a*=0 and b*= 0. For a better comparison with ProfileMaker 5 (GamutView), the values were converted by mapping LUT white to media white. Media white is defined in the profile by Xmw = 0.84552, Ymw =0.87683, Zmw =0.74716. The sequence is algorithmically defined by LABtoXYZ, X = X路(Xmw / Xn ), Y = Y路(Ymw / Yn ), Z = Z路( Zmw/Zn ), XYZtoLAB . The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as white round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 20

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.3 AdobeRGB L*=30 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as white round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 30

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.4 AdobeRGB L*=40 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as white round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 40

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.5 AdobeRGB L*=50 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as black round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 50

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.6 AdobeRGB L*=60 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as black round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 60

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.7 AdobeRGB L*=70 The graphic shows Lab values for AdobeRGB(98) and available values for the CMYK profile ISOcoated_v2_eci.icc as black round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 70

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.8 AdobeRGB L*=80 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as black round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 80

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

9.9 AdobeRGB L*=90 The graphic shows Lab values for AdobeRGB and available values for the CMYK profile ISOcoated_v2_eci.icc as black round dots.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 90

-40

AdobeRGB(98) White D65 Reference D50 Bradford yes Gamma 2.2 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.1 ProPhotoRGB L*=10 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing. See chapter 9.1 and 9.2 for some details how to extract the data from the profile. Media white is defined in the profile by Xmw = 0.84386, Ymw =0.87556, Zmw =0.74486. This profile is used for frequency - modulated printing, like inkjet printing. The gamut is a little larger than that of ISOcoated_v2_eci.icc (previous chapter), but it fits as well in the gamut of AdobeRGB.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 0

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.2 ProPhotoRGB L*=20 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 20

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.3 ProPhotoRGB L*=30 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 30

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.4 ProPhotoRGB L*=40 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 40

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.5 ProPhotoRGB L*=50 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 50

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.6 ProPhotoRGB L*=60 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 60

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.7 ProPhotoRGB L*=70 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 70

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.8 ProPhotoRGB L*=80 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 80

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

10.9 ProPhotoRGB L*=90 The graphic shows Lab values for ProPhotoRGB and available values for the CMYK profile PSO_Coated_NPscreen_ISO12647_eci.icc as black round dots. This is a profile for FM printing.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60 -70 -80 -90

L* = 90

-40

ProPhoto primaries White D50 Reference D50 Bradford no Gamma .8 Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-50 -60 -70 -80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

11.1 3D Views for three RGB-Spaces

No artifacts for Smooth Line Art Off a*

CIE a*b* axes -100 /100 L* 1/ 99

NTSC a*

sRGB a*

11.2 3D Views, Rotated, for sRGB Volumes and wireframes use smoothed height contours L*

b* b* a* a*

sRGB

a*b* axes -100 /100 L* 0/100

a* b*

a* a* b* b* L*

b* a*

11.3 3D Views

CIE a*b* axes -100 /100 L* 0 / 95

NTSC a*

sRGB a*

12. Linear and Standard Nonlinear CIELab The bottom image shows the same 3D view for the sRGB color system as on the previous page. The top image shows a linear transformation,as in chapter 2.4:

L* = 100 Y /Yn a* = 500 (X/Xn - Y/Yn ) b* = 200 (Y/ Yn - Z/Zn )

Here we can see that the colors are too light for low luminance. This is the reason for the introduction of the nonlinear CIELab conversion, though the cubic root law is also not perfect.

sRGB Linear

a*b* axes -100 /100 L* 0 / 95

sRGB Nonlinear

13. Human Gamut in CIELab The human gamut in CIELab is a cone with the apex at the origin of the coordinate system. A threedimensional illustration can be found in [2] as well. Here we see three cross sections at L*= 20, 40 and 60. The axes a* and b* are drawn with lengths Âą 200.

14. Low Chromaticity for sRGB L*=50

-20 - 8 - 6 - 4 - 2 - 0 -8

-6

-4

-2

0 2 4 6 8 20

-2

-4

-6

-8 - 0 - 2 - 4 - 6 - 8

L* = 50

-8

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB Dot mark for out of gamut Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

- 0 - 2 - 4 - 6 - 8

-20

-20 -20 - 8 - 6 - 4 - 2 - 0 -8

-6

-4

-2

0 2 4 6 8

15. sRGB L*=50 with RGB Numbers

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

b* 90 80 70 60 50 40 30 20 0 0 - 0 -20 -30 -40 -50 -60 -70 -80 -90 - 00

00 0 0 6 44 4 0 0 0 0 6 44 4 0 0 0 0 6 44 4 0 0 0 0 6 44 4 0 0 0 0 6 44 42 3 6 0 0 7 44 42 40 4 0 0 7 44 42 62 63 0 0 7 45 42 8 82 0 0 7 45 42 99 00 0 0 7 45 43 6 7 7 0 0 8 45 43 4 34 34 0 0 8 46 43 5 5 0 0 9 46 44 8 69 69 0 0 9 47 44 6 86 709 primaries 86 0 0 White 0 D65 47 45 3 203 Reference D50 204 0 0 Bradford 0 yes 48 46 22 22 Gamma sRGB 0 0 Dot mark for 49 46 9 239 239 out of gamut 0 0 Clipping for 2 50 47 R-Y-G-C-B-M 5 255 255 hexagon 0 0 3 5 48 Outer blue area 5 255 255 human gamut 0 0 4 52 49 5 255 255

L* = 50

32 38 0 29 38 0 25 38 0 8 38 0 2 39 9 0 39 42 0 39 63 0 39 82 0 39 00 0 40 7 0 40 34 0 40 52 0 4 69 0 4 86 0 42 204 0 43 22 0 44 239 0 44 255 0 45 255 0 46 255

67 35 0 66 35 0 64 35 0 62 35 0 58 35 2 53 35 43 44 36 64 3 36 83 0 36 00 0 36 7 0 37 35 0 37 52 0 38 69 0 38 86 0 39 204 0 40 222 0 40 239 0 4 255 0 42 255 0 43 255

90 3 0 89 3 0 87 3 0 86 32 0 83 32 5 80 32 44 75 32 65 69 32 83 59 32 0 45 33 8 5 33 35 0 34 52 0 34 69 0 35 87 0 35 204 0 36 222 0 37 239 0 38 255 0 39 255 0 40 255

08 27 0 07 27 0 06 27 0 05 27 0 03 28 7 0 28 45 97 28 65 92 28 84 86 28 0 77 29 8 65 29 35 47 30 52 0 30 69 0 3 87 0 3 204 0 32 222 0 33 240 0 34 255 0 35 255 0 36 255

24 23 0 24 23 0 23 23 0 22 23 0 20 23 20 8 23 46 5 23 66 23 84 06 24 0 00 24 9 92 25 36 80 25 53 64 26 70 36 26 87 0 27 204 0 28 222 0 29 240 0 30 255 0 3 255 0 32 255

39 7 0 39 7 0 38 7 0 37 8 0 36 8 22 34 8 47 32 8 67 28 8 85 24 9 02 9 9 9 2 9 36 04 20 53 93 20 70 77 2 87 54 22 205 0 23 222 0 24 240 0 25 255 0 26 255 0 27 255

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

53 0 53 0 52 0 5 2 0 50 2 25 49 2 49 47 2 68 44 2 85 40 3 02 36 3 9 30 3 36 23 4 53 4 5 70 03 5 87 88 6 205 66 7 222 6 8 240 0 9 255 0 20 255 0 22 255

67 04 0 66 05 0 66 05 0 65 05 0 64 05 27 63 05 50 6 05 69 58 05 86 55 06 03 5 06 20 46 07 37 40 07 53 33 08 70 24 09 88 2 0 205 97 223 75 2 240 34 3 255 0 4 255 0 6 255

80 96 0 79 96 0 79 97 0 78 97 0 77 97 30 76 97 5 74 97 69 72 98 87 69 98 04 66 98 20 6 99 37 56 00 54 50 00 7 42 0 88 32 02 205 20 03 223 05 04 240 83 06 255 45 07 255 0 09 255

92 87 0 92 87 0 9 87 0 9 87 0 90 87 32 89 87 53 87 88 70 85 88 87 83 89 04 80 89 2 76 90 37 7 90 54 65 9 7 58 92 88 50 93 205 40 94 223 27 96 24 97 255 89 99 255 5 00 255

205 75 0 204 75 0 204 75 0 203 75 4 202 75 34 20 76 54 200 76 7 98 77 88 96 77 05 93 78 2 89 78 38 85 79 55 80 80 7 74 8 88 67 83 206 58 84 223 47 85 24 34 87 255 7 89 255 94 9 255

2 7 59 0 2 6 59 0 2 6 60 0 2 5 60 0 2 5 60 37 2 4 60 55 2 2 6 73 2 6 89 208 62 05 206 63 22 203 64 38 99 65 55 94 66 72 89 67 89 82 69 206 74 7 223 65 73 24 54 75 255 40 77 255 22 79 255

229 35 0 228 35 0 228 35 0 227 35 6 227 36 39 226 36 57 225 37 74 223 38 90 22 39 06 2 8 4 22 2 5 42 39 2 2 44 55 208 46 72 203 48 89 97 50 206 90 52 224 8 55 24 72 58 255 60 60 255 45 63 255

240 0 0 240 0 0 240 0 0 239 0 20 239 0 4 238 0 58 237 0 75 235 0 9 233 0 07 23 0 23 228 0 39 225 0 56 22 0 73 2 6 0 90 2 8 207 205 7 224 97 23 242 88 29 255 78 35 255 65 40 255

252 0 0 252 0 0 25 0 0 25 0 25 250 0 43 249 0 60 248 0 76 247 0 92 245 0 08 243 0 24 24 0 40 237 0 56 234 0 73 230 0 90 225 0 207 2 9 0 224 2 2 0 242 204 0 255 95 0 255 84 0 255

0 20 30 40 50 60 70 80 90

90 80 70 60 50 40 30 20 0 0 - 0 -20 -30 -40 -50 -60 -70 -80 -90 - 00

16.1 PostScript Kernels /PrimsCie {/txtP (CIE primaries) def /xr 0.73467 def /yr 0.26533 def /xg 0.27376 def /yg 0.71741 def /xb 0.16658 def /yb 0.00886 def } def /Prims709 {/txtP (709 primaries) def /xr 0.64000 def /yr 0.33000 def /xg 0.30000 def /yg 0.60000 def /xb 0.15000 def /yb 0.06000 def } def /PrimsNTSC {/txtP (NTSC /xr 0.67000 /xg 0.21000 /xb 0.14000 } def

primaries) def def /yr 0.33000 def def /yg 0.71000 def def /yb 0.08000 def

/PrimsWide {/txtP (WideGamut /xr 0.734700 def /xg 0.115173 def /xb 0.156608 def } def

primaries) def /yr 0.265299 def /yg 0.826432 def /yb 0.017658 def

/PrimsProP {/txtP (ProPhoto primaries) def /xr 0.734698 def /yr 0.265302 def /xg 0.159599 def /yg 0.840401 def /xb 0.036600 def /yb 0.000107 def } def /PrimsAd98 {/txtP (AdobeRGB(98)) def /xr 0.64000 def /yr 0.33000 def /xg 0.21000 def /yg 0.71000 def /xb 0.15000 def /yb 0.06000 def } def /PrimsOpti {/txtP (OptiRGB) def /xr 0.6658 def /yr 0.3340 def %610 /xg 0.1929 def /yg 0.7816 def %535 /xb 0.1355 def /yb 0.0399 def %465 } def /WhiteEqE {/xw 0.3333 def /yw 0.3333 /txtW (Eq.Energy ) def } def /WhiteD65 {/xw 0.3127 def /yw 0.3290 /txtW (D65) def } def /WhiteNTSC % Illuminant C {/xw 0.3100 def /yw 0.3160 /txtW (NTSC) def } def /White3000K % R.W.G.Hunt, {/xw 0.4368 def /yw 0.4041 /txtW (3000K) def } def /White4000K {/xw 0.3804 def /yw 0.3767 /txtW (4000K) def } def /WhiteD50 {/xw 0.3457 def /yw 0.3585 /txtW (D50) def } def /White6000K

def

def Measuring Colours def

def

16.2 PostScript Kernels {/xw 0.3220 def /yw /txtW (6000K) def } def /White7000K {/xw 0.3063 def /yw /txtW (7000K) def } def /White8000K {/xw 0.2952 def /yw /txtW (8000K) def } def /White9300K % {/xw 0.2857 def /yw /txtW (9300K) def } def /RefEqE {/xn 0.3333 def /yn /txtN (Eq.Energy ) } def /RefD65 {/xn 0.3127 def /yn /txtN (D65) def } def /RefNTSC {/xn 0.3100 def /yn /txtN (NTSC) def } def /RefD50 {/xn 0.3457 def /yn /txtN (D50) def } def

0.3318 def

0.3165 def

0.3048 def

0.2941 def % Wyszecki+Stiles interpolated

0.3333 def def 0.3290 def

0.3160 def

0.3585 def

/MakeBrad {% ICC-Spec p.110 % Cone = CX*X; X = XC*Cone % Cone Response /CX11 0.8951 def /CX12 0.2664 def /CX13 -0.1614 def /CX21 -0.7502 def /CX22 1.7135 def /CX23 0.0367 def /CX31 0.0389 def /CX32 -0.0685 def /CX33 1.0296 def % Inverse Cone Response /D CX22 CX33 mul CX23 CX32 mul sub CX11 mul CX21 CX33 mul CX23 CX31 mul sub CX12 mul sub CX21 CX32 mul CX22 CX31 mul sub CX13 mul add def /XC11 CX22 CX33 mul CX23 CX32 mul sub D div def /XC12 CX12 CX33 mul CX13 CX32 mul sub D div neg def /XC13 CX12 CX23 mul CX13 CX22 mul sub D div def /XC21 CX21 CX33 mul CX23 CX31 mul sub D div neg def /XC22 CX11 CX33 mul CX13 CX31 mul sub D div def /XC23 CX11 CX23 mul CX13 CX21 mul sub D div neg def /XC31 CX21 CX32 mul CX22 CX31 mul sub D div def /XC32 CX11 CX32 mul CX12 CX31 mul sub D div neg def /XC33 CX11 CX22 mul CX12 CX21 mul sub D div def % Source /Yws 1 def /zw 1 xw sub yw sub def /Xws xw yw div Yws mul def /Zws zw yw div Yws mul def % PCS /Ywp 1 def /zn 1 xn sub yn sub def /Xwp xn yn div Ywp mul def /Zwp zn yn div Ywp mul def % Cone Source /Rs CX11 Xws mul CX12 /Gs CX21 Xws mul CX22 /Bs CX31 Xws mul CX32 % Cone PCS /Rp CX11 Xwp mul CX12 /Gp CX21 Xwp mul CX22 /Bp CX31 Xwp mul CX32 /a11 Rp Rs div def

Yws mul add CX13 Zws mul add def Yws mul add CX23 Zws mul add def Yws mul add CX33 Zws mul add def Ywp mul add CX13 Zwp mul add def Ywp mul add CX23 Zwp mul add def Ywp mul add CX33 Zwp mul add def

16.3 PostScript Kernels /a22 Gp Gs div def /a33 Bp Bs div def % Diag(aii)*CX /X11 a11 CX11 mul def /X12 a11 CX12 mul def /X13 a11 CX13 mul def /X21 a22 CX21 mul def /X22 a22 CX22 mul def /X23 a22 CX23 mul def /X31 a33 CX31 mul def /X32 a33 CX32 mul def /X33 a33 CX33 mul def % Bradford % BM = XC*Diag(aii)*CX /BM11 XC11 X11 mul XC12 /BM12 XC11 X12 mul XC12 /BM13 XC11 X13 mul XC12 /BM21 XC21 X11 mul XC22 /BM22 XC21 X12 mul XC22 /BM23 XC21 X13 mul XC22 /BM31 XC31 X11 mul XC32 /BM32 XC31 X12 mul XC32 /BM33 XC31 X13 mul XC32

X21 X22 X23 X21 X22 X23 X21 X22 X23

mul mul mul mul mul mul mul mul mul

add add add add add add add add add

XC13 XC13 XC13 XC23 XC23 XC23 XC33 XC33 XC33

X31 X32 X33 X31 X32 X33 X31 X32 X33

mul mul mul mul mul mul mul mul mul

add add add add add add add add add

% Inverse Bradford /D BM22 BM33 mul BM23 BM32 mul sub BM11 BM21 BM33 mul BM23 BM31 mul sub BM12 BM21 BM32 mul BM22 BM31 mul sub BM13 /MB11 BM22 BM33 mul BM23 BM32 mul sub D /MB12 BM12 BM33 mul BM13 BM32 mul sub D /MB13 BM12 BM23 mul BM13 BM22 mul sub D /MB21 BM21 BM33 mul BM23 BM31 mul sub D /MB22 BM11 BM33 mul BM13 BM31 mul sub D /MB23 BM11 BM23 mul BM13 BM21 mul sub D /MB31 BM21 BM32 mul BM22 BM31 mul sub D /MB32 BM11 BM32 mul BM12 BM31 mul sub D /MB33 BM11 BM22 mul BM12 BM21 mul sub D

mul mul mul div div div div div div div div div

sub add def def neg def def neg def def neg def def neg def def

def def def def def def def def def

% Bradford matrix XYZ(D50)=BM*XYZ(D65) %/BM11 1.0479 def /BM12 0.0229 def /BM13 -0.0502 def %/BM21 0.0296 def /BM22 0.9904 def /BM23 -0.0171 def %/BM31 -0.0092 def /BM32 0.0151 def /BM33 0.7519 def % XYZ(D50)=BM*XYZ(D65) } def /PrimToMat { % matrix CR for XYZ(WP)=CR*RGB(WP) /zr 1 xr sub yr sub def /zg 1 xg sub yg sub def /zb 1 xb sub yb sub def /zw 1 xw sub yw sub def /zn 1 xn sub yn sub def /D xr xb sub yg yb sub mul yr yb sub /U xw xb sub yg yb sub mul yw yb sub /V xr xb sub yw yb sub mul yr yb sub /u U D div def /v V D div def /w 1 u sub v sub def % XYZ(WP)=CR(WP)*RGB(WP) /CR11 u xr mul yw div def /CR12 v xg /CR21 u yr mul yw div def /CR22 v yg /CR31 u zr mul yw div def /CR32 v zg Brad {% XR(D50)=BM*CR(D65) /XR11 BM11 CR11 mul /XR12 BM11 CR12 mul /XR13 BM11 CR13 mul /XR21 BM21 CR11 mul /XR22 BM21 CR12 mul /XR23 BM21 CR13 mul /XR31 BM31 CR11 mul /XR32 BM31 CR12 mul /XR33 BM31 CR13 mul {% XR(D65)=CR(D65)

BM12 BM12 BM12 BM22 BM22 BM22 BM32 BM32 BM32

CR21 CR22 CR23 CR21 CR22 CR23 CR21 CR22 CR23

mul mul mul mul mul mul mul mul mul

xg xb sub mul sub def xg xb sub mul sub def xw xb sub mul sub def

add add add add add add add add add

mul yw div def /CR13 w xb mul yw div def mul yw div def /CR23 w yb mul yw div def mul yw div def /CR33 w zb mul yw div def

BM13 BM13 BM13 BM23 BM23 BM23 BM33 BM33 BM33

CR31 CR32 CR33 CR31 CR32 CR33 CR31 CR32 CR33

mul mul mul mul mul mul mul mul mul

add add add add add add add add add

def def def def def def def def def }

16.4 PostScript Kernels /XR11 CR11 def /XR12 CR12 def /XR13 CR13 def /XR21 CR21 def /XR22 CR22 def /XR23 CR23 def /XR31 CR31 def /XR32 CR32 def /XR33 CR33 def } ifelse % Inverse of XR /D XR22 XR33 mul XR23 XR32 mul sub XR11 mul XR21 XR33 mul XR23 XR31 mul sub XR12 mul sub XR21 XR32 mul XR22 XR31 mul sub XR13 mul add def /RX11 XR22 XR33 mul XR23 XR32 mul sub D div def /RX12 XR12 XR33 mul XR13 XR32 mul sub D div neg def /RX13 XR12 XR23 mul XR13 XR22 mul sub D div def /RX21 XR21 XR33 mul XR23 XR31 mul sub D div neg def /RX22 XR11 XR33 mul XR13 XR31 mul sub D div def /RX23 XR11 XR23 mul XR13 XR21 mul sub D div neg def /RX31 XR21 XR32 mul XR22 XR31 mul sub D div def /RX32 XR11 XR32 mul XR12 XR31 mul sub D div neg def /RX33 XR11 XR22 mul XR12 XR21 mul sub D div def /Yw 1 def /Xw xw yw div Yw mul def /Zw zw yw div Yw mul def /Yn 1 def /Xn xn yn div Yn mul def /Zn zn yn div Yn mul def } def /LABtoRGB {%/c0 1 3 div def Actual definition in main program %/c1 0.008856 def %/c2 7.787 def %/c3 16 116 div def %/c4 0.206893 def /Y1 L* 0.16 add 1.16 div def /X1 a* 5.0 div Y1 add def /Z1 Y1 b* 2.0 div sub def /X X1 c4 le {X1 c3 sub c2 div }{ X1 3 exp } ifelse Xn mul def /Y Y1 c4 le {Y1 c3 sub c2 div }{ Y1 3 exp } ifelse Yn mul def /Z Z1 c4 le {Z1 c3 sub c2 div }{ Z1 3 exp } ifelse Zn mul def /R X RX11 mul Y RX12 mul add Z RX13 mul add def /G X RX21 mul Y RX22 mul add Z RX23 mul add def /B X RX31 mul Y RX32 mul add Z RX33 mul add def } bind def /RGBtoLAB {%/c0 1 3 div def Actual definition in main program %/c1 0.008856 def %/c2 7.787 def %/c3 16 116 div def %/c4 0.206893 def /X R XR11 mul G XR12 mul add B XR13 mul add def /Y R XR21 mul G XR22 mul add B XR23 mul add def /Z R XR31 mul G XR32 mul add B XR33 mul add def /X1 X Xn div dup c1 le { c2 mul c3 add }{ c0 exp } ifelse def /Y1 Y Yn div dup c1 le { c2 mul c3 add }{ c0 exp } ifelse def /Z1 Z Zn div dup c1 le { c2 mul c3 add }{ c0 exp } ifelse def /a* X1 Y1 sub 5.0 mul def /b* Y1 Z1 sub 2.0 mul def /ga* a* 1.05 add 100 mm mul def /gb* b* 1.05 add 100 mm mul def } bind def /IGamma { /iga 1 gam div def /og false def % out of gamut R 0 lt { /R 0 def /og true def } if G 0 lt { /G 0 def /og true def } if B 0 lt { /B 0 def /og true def } if R 1 gt { /R 1 def /og true def } if G 1 gt { /G 1 def /og true def } if B 1 gt { /B 1 def /og true def } if gam 2.4 ne {/R R iga exp def /G G iga exp def /B {/R R dup 0.00304 lt {12.92 mul }{iga /G G dup 0.00304 lt {12.92 mul }{iga /B B dup 0.00304 lt {12.92 mul }{iga R G B setrgbcolor } bind def /xyYtoLAB

B iga exp exp 1.055 exp 1.055 exp 1.055

def mul mul mul

} 0.055 sub } ifelse def 0.055 sub } ifelse def 0.055 sub } ifelse def } ifelse

16.5 PostScript Kernels % input x,y,Y { /z 1 x sub y sub def /X x y div Y mul def /Z z y div Y mul def /R X RX11 mul Y RX12 mul add Z RX13 mul add def /G X RX21 mul Y RX22 mul add Z RX23 mul add def /B X RX31 mul Y RX32 mul add Z RX33 mul add def /max R def G max gt {/max G def } if B max gt {/max B def } if /R R max div def /G G max div def /B B max div def RGBtoLAB } bind def % ----------------------------------------------%—Choose Gamma /G 1 def G 0 eq {/gam 1.8 def} if % ProPhoto G 1 eq {/gam 2.2 def} if G 2 eq {/gam 2.4 def} if % sRGB %—Choose one /P 0 def P 0 eq { PrimsCie P 1 eq { Prims709 P 2 eq { PrimsNTSC P 3 eq { PrimsWide P 4 eq { PrimsAd98 P 5 eq { PrimsProP

} } } } } }

%—Choose one /W 0 def W 0 eq { WhiteEqE W 1 eq { WhiteD65 W 2 eq { WhiteNTSC W 3 eq { White3000K W 4 eq { White4000K W 5 eq { WhiteD50 W 6 eq { White6000K W 7 eq { White7000K W 8 eq { White8000K W 9 eq { White9300K

if if if if if if

%—Choose one /N 5 def N 0 eq { RefEqE } N 1 eq { RefD65 } N 2 eq { RefNTSC} N 5 eq { RefD50 }

} } } } } } } } } }

if if if if if if if if if if

% also Wide Gamut and ProPhoto

if if if if

%—Choose one /B 1 def B 0 eq { /Brad false def } if B 1 eq { /Brad true def } if %—Choose one /L 5 def L 0 eq {/L* 0.01 def} if L 1 eq {/L* 0.1 def} if L 2 eq {/L* 0.2 def} if L 3 eq {/L* 0.3 def} if L 4 eq {/L* 0.4 def} if L 5 eq {/L* 0.5 def} if L 6 eq {/L* 0.6 def} if L 7 eq {/L* 0.7 def} if L 8 eq {/L* 0.8 def} if L 9 eq {/L* 0.9 def} if L 10 eq {/L* 0.99 def} if MakeBrad PrimToMat

17.1 Mapping CIELab to xyY Clipped for human gamut

A new working space is introduced:

L = 10, 20 .. 90 Radius = 10, 20 ..120 Angle = 0, 15 .. 345째

OptiRGB xr = 0.6658 yr = 0.3340 610nm xg = 0.1929 yg = 0.7816 535nm xb = 0.1355 yb = 0.0399 465nm Gamma=2.2 D65

Lines of constant radius for L=50 Straight lines a=0 or b=0 .0 y 0.9 5 5

0.8

520 525

5 0

530

535

OptiRGB

0.7

540 545 550

505

555 AdobeRGB(98)

560

0.6

565 570

500

0.4 0.3 0.2

575

sRGB

0.5

580 585 590 595 600 605 6 0 620 635 700

495

490

485 480

0. 0.0 0.0

475 470 460 380

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 x .0

17.2 Mapping CIELab to xyY Clipped for human gamut L = a = b =

10, 20 .. 90 -120,-110 .. +120 -120,-110 .. +120

Straight lines a=0 or b=0

.0 y 0.9 5 5

0.8

520 525

5 0

530

535

OptiRGB

0.7

540 545 550

505

555 AdobeRGB(98)

560

0.6

565 570

500

0.4 0.3 0.2

575

sRGB

0.5

580 585 590 595 600 605 6 0 620 635 700

495

490

485 480

0. 0.0 0.0

475 470 460 380

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 x .0

17.3 Mapping CIELab to xyY Clipped for the xy-unit-square. Many colors are out of human gamut (chapter 13). Random values L = 5 .. 95 a = -120 .. +120 b = -120 .. +120 Straight lines a=0 or b=0

.0 y 0.9 5 5

0.8

520 525

5 0

530

535

OptiRGB

0.7

540 545 550

505

555 AdobeRGB(98)

560

0.6

565 570

500

0.4 0.3 0.2

575

sRGB

0.5

580 585 590 595 600 605 6 0 620 635 700

495

490

485 480

0. 0.0 0.0

475 470 460 380

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 x .0

18. Number of Different Colors Test images sRGB with 1 million pixels each are converted to CIELab. The numbers in CIELab are rounded for 256/256/256 or 100/256/256 or 50/128/128 different levels. The CIELab values are converted back to sRGB, everything with double precision. The number of different colors in sRGB is counted before and after the conversion. The first test image (not shown) contains random values for sRGB. The second is this portrait, cropped for height and width 1000 pixels.

Test results Mode Pixels Colors Source sRGB Colors 256/256/256 Colors 100/256/256 Colors 50/128/128

Random 1.000.000 969.864 795.538 611.904 146.712

Portrait 1.000.000 182.629 89.451 47.006 9.485

The random image uses the whole sRGB space, the portrait only a small part. Therefore a loss of levels by percentage because of quantization is more likely for the portrait. Number N of colors in CIELab for sRGB, aRGB = AdobeRGB(98) and pRGB=ProPhotoRGB: N=0 Define RGB space For L*=0 To 100 Step 2 Do For a*=-128 To +128 Step 2 Do For b*=-128 To +128 Step 2 Do Begin Convert L*,a*,b* into R,G,B If R,G,B in [0...255] Then N=N+1 End N=8*N

Number N sRGB 832.752 aRGB 1.208.912 pRGB 2.659.728

19.1 HLS -Hue for sRGB in CIELab The graphic shows lines with constant HLS- Hue H=0°, 30°, ..., 330° with varying HLSSaturation S=0...1 for three HLS-Lightnesses L=0.25, 0.50, 0.75 in one plane a*,b*. Lines for Hues k·60° hit the primaries RGB and the secondaries CMY at S=1. The inputs H,L,S are here converted by Foley-HLS [9] into linear RGB, whereas HLS to RGB delivers traditionally gamma encoded nonlinear values R‘G‘B‘. Lines with constant HLS-Hue appear considerably curved in a CIELab plane a*, b*. Perceived Hue can be defined by Munsell colors. Lines with constant Munsell hue appear curved in CIELab as well. The dotted line is an interpolation path, see next page.

- 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90 00

- 0

-20

-30

-40 -50 -60

L* all

-40

709 primaries White D65 Reference D50 Bradford yes Gamma sRGB

-50 -60

-70 -80 -90

-70

Clipping for R-Y-G-C-B-M hexagon Outer blue area human gamut

-80 -90

- 00

- 00 - 00 -90 -80 -70 -60 -50 -40 -30 -20 - 0 0

0 20 30 40 50 60 70 80 90

19.2 HLS -Hue for sRGB in CIELab It has been often observed, that some blues which are out of gamut for a printer were mapped to in-gamut blues with a magenta tint [10]. The graphic shows two gradients with endpoints Lab1=35/55/-100 RGB1=47/47/250 (blue) and Lab2=35/0/0 RGB2=82/82/82 (gray). The upper gradient was made in sRGB, the lower in Lab. The sRGB gradient shows already a magenta tint though all interpolated colors have equal values R=G, which should result in less saturated blue without a tint. According to [11] one has to take into account optical illusions: Abney effect: hue changes with colorimetric purity (here). Bezold-Br端cke effect: hue changes with luminance. The Lab gradient shows an even stronger magenta tint. On the previous page one can see a linear interpolation (dotted line) from Lab1 to Lab2. This interpolation path goes through magenta area. Therefore a gamut compression in planes of constant Lab hue is not ideal, but the other effects should not be ignored.

RGB

Lab

20. 1 References [1]

R.W.G.Hunt Measuring Colour Fountain Press England 1998

[2] G.Wyszecki + W.S.Stiles Color Science John Wiley & Sons, New York ,..., 1982 [3] References for Color Science http://www.fho-emden.de/~hoffmann/ciexyz29082000.pdf [4] References for PostScript http://www.fho-emden.de/~hoffmann/pstutor22112002.pdf [5] Everything about Color and Computers http://www.efg2.com [6]

M.Nielsen + M.Stokes The Creation of the sRGB ICC Profile http://www.srgb.com/c55.pdf Year unknown, after 1998

[7] [8]

International Color Consortium http://www.color.org File Format for Color Profiles / newest version http://www.color.org/icc_specs2.xalter

[9] G.Hoffmann Color Order Systems RGB/HLS/HSB http://www.fho-emden.de /~hoffmann/hlscone03052001.pdf [10] http://www.brucelindbloom.com [11] M.D.Fairchild Color Appearance Models John Wiley & Sons, Ltd England, 2005 [12] Jรกn Moroviฤ Color Gamut Mapping John Wiley & Sons, Ltd 2008

20. 2 References [13] http://www.eci.org/doku.php?id=en:downloads [14] http://www.fogra.org/products-de/icc/Readme04d.pdf [15] http://www.fogra.org/products-de/icc/FograCharDaten_ECIProfile.pdf [16] http://www.eci.org/doku.php?id=de:start

This doc:

http://www.fho-emden.de/~hoffmann/cielab03022003.pdf

December 17 / 2008 the doc was converted from PageMaker to InDesign. Minor errors cannot be excluded.

Gernot Hoffmann December 19 / 2008 Website Load Browser / Click here 63